associated_legendre

Overloads

Name	Description
associated_legendre(integer n, integer m, bool x) -> real	Evaluates the associated Legendre polynomial of degree n and order m at the given position. The associated Legendre polynomials are defined as:...
associated_legendre(integer n, integer m, real x) -> real	Evaluates the associated Legendre polynomial of degree n and order m at the given position. The associated Legendre polynomials are defined as:...
associated_legendre(integer n, integer m, integer x) -> real	Evaluates the associated Legendre polynomial of degree n and order m at the given position. The associated Legendre polynomials are defined as:...

associated_legendre(integer n, integer m, bool x) -> real

Evaluates the associated Legendre polynomial of degree n and order m at the given position. The associated Legendre polynomials are defined as:

$$P_{n}^{m}(x) = (-1)^{m} \frac{(n-m)!}{(n+m)!} \frac{d^{m}}{dx^{m}} P_{n}(x)$$

Parameters

• n: The degree of the polynomial.
• m: The order of the polynomial.
• x: The value at which the function is evaluated.

associated_legendre(integer n, integer m, real x) -> real

Evaluates the associated Legendre polynomial of degree n and order m at the given position. The associated Legendre polynomials are defined as:

$$P_{n}^{m}(x) = (-1)^{m} \frac{(n-m)!}{(n+m)!} \frac{d^{m}}{dx^{m}} P_{n}(x)$$

Parameters

• n: The degree of the polynomial.
• m: The order of the polynomial.
• x: The value at which the function is evaluated.

associated_legendre(integer n, integer m, integer x) -> real

Evaluates the associated Legendre polynomial of degree n and order m at the given position. The associated Legendre polynomials are defined as:

$$P_{n}^{m}(x) = (-1)^{m} \frac{(n-m)!}{(n+m)!} \frac{d^{m}}{dx^{m}} P_{n}(x)$$

Parameters

• n: The degree of the polynomial.
• m: The order of the polynomial.
• x: The value at which the function is evaluated.